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Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping. (English) Zbl 1250.35134
The model consists of a wave equation on a bounded domain, coupled with a pointwise damped harmonic oscillator equation, with boundary conditions on the interface. The purpose of the paper is to study the existence, uniqueness and uniform decay of finite energy solutions to the considered model. In case some specific conditions are fulfilled, the existence and uniqueness of weak solutions to the system, continuously depending on initial data, are proved. Under additional assumptions, decay rates for the energy functional for solutions of the PDE system are obtained. Techniques from nonlinear semigroup theory are used. For similar investigations by the author, see [the author and B. Said-Hourari, J. Differ. Equations 252, No. 9, 4898–4941 (2012; Zbl 1250.35135)].

MSC:
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L05 Wave equation
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35B40 Asymptotic behavior of solutions to PDEs
35D30 Weak solutions to PDEs
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